Hose clamps of the aforedescribed type in which the inner end segment has retaining and bracing hooks which, in indexing of the band to the circumference of the hose, are received in corresponding openings in the outer band segment, are used to press a hose tightly against a support fitting over which the hose can be engaged. The inner end of the outer band segment can be formed with an outwardly projecting step having a height corresponding to that of the thickness of the band (see German Patent Documents DE 30 17 667 C2 and DE 30 17 666 C2). These hose clamps provide an inner surface of the band or the ring formed by the engagement of the inner segment in the outer segment which is substantially gap-free so that leakage of less yieldable plastic hoses or tubing to which the clamp can be applied, is avoided or minimized. Such hoses are commonly used in the automotive industry as, for example, axle sleeves and gasoline lines.